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The Compound Pendulum

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The Compound Pendulum


  • To confirm that a metre rule behaves as a compound pendulum when oscillating;
  • To determine the acceleration due to gravity using a compound pendulum.


Sources used in research of the above tasks are:

  1. A Text-Book of Practical Physics - William Watson; page 129
  2. Laboratory Physics - JH Avery & AWK Ingram; page 69
  3. Intermediate Physics - CJ Smith; page 50
  4. The Text-Book of General Physics - GR Noakes; page 394
  5. Intermediate Mechanics - D Humphrey; page 60
  6. Introduction to Physics for Scientists and Engineers (Second Edition) - Frederick J. Bueche; page 222
  7. http://www.physics.mun.ca/~cdeacon/labs/simonfraser.pdf
  8. http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html
  9. http://en.wikipedia.org/wiki/Acceleration_due_to_gravity
  10. http://geophysics.ou.edu/solid_earth/notes/potential/igf.htm
  11. http://www.gorissen.info/Pierre/maps/googleMapLocationv4.php
  12. http://en.wikipedia.org/wiki/Reaction_time

Where direct quotation is made from a source, the source number is shown in superscript after the preceding italicised quote, e.g. ‘quote’4.

The compound pendulum is defined as: ‘a rigid body of any shape and internal structure which is free to turn about a fixed horizontal axis, the only external forces being those due to gravity and the reaction of the axis on the body’ 3. In this investigation a wooden metre rule with holes drilled at various positions down its centre, pivoted on a pin, will act as the compound pendulum.

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The value for k is a constant, and consequently can be ignored, causing the equation to take on the form:

T²h = 4π² h²


This equation relates to that of the simple pendulum, the period of which can be found by 8:

T = 2π  h


When rearranged into the form y = mx + c, it is clearly visible that the equation for the simple pendulum has been multiplied through by h to form the equation for the compound pendulum:

Preliminary Work:

A wooden metre rule drilled through its centre at 0.05m intervals was suspended freely on a pin after ensuring that the centre of gravity was at 0.5m along the metre rule. This was achieved by applying mass, in the form of blu-tack, to one end of the rule when it was suspended at 0.5m until it reached equilibrium and balanced - ‘The position of the centre of gravity can be determined with sufficient accuracy by balancing the pendulum’ 1 The force of gravity ‘can be considered as concentrated at the centre of gravity’ 6 so this must be found to determine h, and hence determine the value for g.  

A number of oscillations were timed for a range of values for h to decide upon an acceptable range of lengths and number of oscillations for the main experiment. Any possible

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Add blu-tack to one end of the metre rule until it balances horizontally without moving. The centre of gravity of the metre rule is now at 50cm along its length. Suspend the metre rule on the pin at 0.05m from the centre of gravity (i.e. at 45 cm along the metre rule)Cover the exposed end of the pin with another cork. Do not push all the way through.Attach the card to the stand with blu-tack ensuring that the vertical timing line is in line with the retort stand. Displace the metre rule so that it lines up with the starting line on the card. Release the pendulum and begin timing as it passes the vertical retort stand.Stop the timer after 15 oscillations as the pendulum passes the retort stand. (One complete oscillation is from when the pendulum passes the stand to it’s extreme of motion at one side, back past the stand to the other extreme and then back to the stand [See Diagram B (above)])Record the time.Repeat steps 10 - 13 for the same length twice. Carry out additional repeats if any values are more than 0.15s from the others.Repeat steps 10 - 14 for lengths of: 0.1m, 0.15m. 0.2m, 0.25m, 0.3m, 0.35m, 0.4m, and 0.45m from the centre of gravity.For each length of the pendulum, h:
  • Calculate the average time for 15 oscillations (addition of the values then division by 3)
  • Divide the average time by 15 to give the time period
  • Calculate T²h
  • Calculate h²

And tabulate the results with these calculated values.

17. Plot a graph of T²h against h².

...read more.

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Response to the question

The candidate has not completed the work so has not answered the question. However, this is a great start. The explanation of theory is good, an important step that is often left until conclusions or sometimes omitted at A-level and ...

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Response to the question

The candidate has not completed the work so has not answered the question. However, this is a great start. The explanation of theory is good, an important step that is often left until conclusions or sometimes omitted at A-level and should not be. The equation should definitely be in there but doesn't need each stage of rearranging showing, if you feel there is a need to show a proof it should be in an appendix. The method seemed reasonable with a clear understanding of how to limit sources of inaccuracies.

Level of analysis

The text has good, relevant physics throughout. It contains good use of references, though these are usually placed at the end of the report. There was no graph, uncertainties or final answer, which made the report less useful.

Quality of writing

The spelling, punctuation and grammar appear to be perfect or very close. It is pleasing to see good use of relevant scientific terms being used correctly.

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